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LIMITED MEMORY BFGS METHOD BY USING LINEAR INDEPENDENT SEARCH DIRECTIONS
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作者 倪勤 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2001年第2期236-239,共4页
The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, thi... The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, this new method determines the new update by applying the updating formula m times to an initial positive diagonal matrix using the m previous pairs of the change in iteration and gradient. Besides the most recent pair of the change, which guarantees the quadratic termination, the choice of the other ( m -1) pairs of the change in the new method is dependent on the degree of numerical linear independence of previous search directions. In addition, the numerical linear independence theory is further discussed and the computation of the degree of linear independence is simplified. Theoretical and numerical results show that this new modified method improves efficiently the standard limited memory method. 展开更多
关键词 unconstrained optimization limited memory method BFGS method degree of linear independence
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Traditional El Nio and El Ni o Modoki Revisited:Is El Nio Modoki Linearly Independent of Traditional El Nio? 被引量:7
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作者 LI Gen REN Bao-Hua YANG Cheng-Yun ZHENG Jian-Qiu 《Atmospheric and Oceanic Science Letters》 2010年第2期70-74,共5页
The present study revisited the first two leading modes of tropical Pacific sea surface temperature anomalies (SSTA) during the period of 1979-2008. It is suggested that the so-called El Nino Modoki, which is captur... The present study revisited the first two leading modes of tropical Pacific sea surface temperature anomalies (SSTA) during the period of 1979-2008. It is suggested that the so-called El Nino Modoki, which is captured by the second mode, exists objectively and exhibits obvious differences from traditional El Nifio, which is captured by the first mode, in terms of its spatial characteristics. Furthermore, the authors found that El Nino Modoki is linearly independent of traditional El Nino; hence, it cannot be described as part of the traditional El Nino evolution, and vice versa. 展开更多
关键词 El Nifio El Nifio Modoki linear independence
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LINEAR INDEPENDENCE OF THE INTEGER TRANS-LATES OF COMPACTLY SUPPORTED DISTRIBU-TIONS AND REFINABLE VECTORS
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作者 Sun QiyuDept. of Math.,National University of Singapore,10 Kent Ridge Crescent,Singapore 119260,Singapore. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第4期381-396,共16页
In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.
关键词 Global linear independence local linear independence refinable vector invariant space.
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SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION
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作者 潘娟 周云华 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1382-1402,共21页
We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existe... We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existence of cover measures, an ergodic theorem about mean linear independence and the style number, and a variational principle for style numbers and independence numbers. We also study the relationship between the entropy of base systems and that of their bundle systems. 展开更多
关键词 mean linear independence style number independence number ENTROPY
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Why Are There as Many Elements in the Cantor Set as There Are Real Numbers?
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作者 Wenbing Wu Xiaojian Yuan 《Open Journal of Applied Sciences》 2023年第11期2183-2185,共3页
There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish betw... There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph;otherwise, it is a linear correlation. 展开更多
关键词 Cantor Ternary Set linear Independence Vector linear Algebra
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A new algorithm for designing developable Bézier surfaces 被引量:3
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作者 ZHANG Xing-wang WANG Guo-jin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期2050-2056,共7页
A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient condition... A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper. 展开更多
关键词 Bézier surfaces Developable surfaces Bemstein basis linear independence Characteristic equations
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NUAT T-splines of odd bi-degree and local refinement 被引量:1
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作者 DUAN Xiao-juan WANG Guo-zhao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第4期410-421,共12页
This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces (NUAT T-splines for short) of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-... This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces (NUAT T-splines for short) of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic- trigonometric B-spline surfaces (NUAT B-spline surfaces). Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd hi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix. 展开更多
关键词 odd bi-degree non-uniform algebraic-trigonometric T-spline local refinement blending function linear independence.
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The optimum linear data fusion of independent observation data 被引量:1
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作者 LI Qinu (Institute of Acoustics, Academia Sinica Beijing 100080) 《Chinese Journal of Acoustics》 2001年第1期18-24,共7页
Data Fusion is one of the attractive topic in sonar signal processing. Decision level data fusion of multi-sensor (multi-array) system is described in this paper. The optimum linear data fusion algorithm for N indepen... Data Fusion is one of the attractive topic in sonar signal processing. Decision level data fusion of multi-sensor (multi-array) system is described in this paper. The optimum linear data fusion algorithm for N independent observation data is derived. It is proved that the estimation error of optimum data fusion is not greater than that of individual components. The expression of estimation error and weight coefficients are presented. The results of numerical calculation and some examples are illustrated. The effect of input signal to noise ratio for the data fusion is described. 展开更多
关键词 The optimum linear data fusion of independent observation data
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On the Linear Independence and Partition of Unity of Arbitrary Degree Analysis-Suitable T-splines 被引量:7
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作者 Jingjing Zhang Xin Li 《Communications in Mathematics and Statistics》 SCIE 2015年第3期353-364,共12页
Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aid... Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aided Geom Design 29:63-76,2012;Scott et al.Comput Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending functions.We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation. 展开更多
关键词 T-SPLINES Analysis-suitable T-splines linear independence Partition of unity Isogeometric analysis
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Linear independence of a finite set of time-frequency shifts
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作者 Dengfeng LI 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第4期501-509,共9页
This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L2 function.Firstly,background and motivation for the conjecture are p... This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L2 function.Firstly,background and motivation for the conjecture are provided.Secondly,the main progress of this linear independence in the past twenty five years is reviewed.Finally,the partial results of the high dimensional case and other cases for the conjecture are briefly presented. 展开更多
关键词 Time-frequency shift Gabor frame WAVELET linear independence
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LINEAR INDEPENDENCE OF REFINABLEDISTRIBUTIONS SUPPORTED ON[0, 2]×[0, 2]
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作者 毕宁 孙颀彧 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1998年第4期388-395,共8页
In this paper a necessary and sufficient condition on symbol is given for linear independence of refinable distributions supported on [0,2]×[0,2].
关键词 Refinable distribution SYMBOL linear independence
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CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS 被引量:3
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作者 SUN QIYU Department of Mathematics, University of Houston, Houston, TX 77204, USA. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore. 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第3期367-386,共20页
In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on th... In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on the convergence to characterizing compactly supportedrefinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriateinitial to guarantee the convergence of the cascade algorithm (see Theorem 4.2). 展开更多
关键词 Cascade algorithm Cascade operator Refinable distribution Shift-invariant space linear independent shifts Stable shifts Fractional Sobolev space
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SOME PROPERTIES FOR ANALYSIS-SUITABLE T-SPLINES 被引量:3
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作者 Xin Li 《Journal of Computational Mathematics》 SCIE CSCD 2015年第4期428-442,共15页
Analysis-suitable T-splines (AS T-splines) are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric ana... Analysis-suitable T-splines (AS T-splines) are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis (IGA) oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines. 展开更多
关键词 T-SPLINES linear independence iso-geometric analysis Analysis-suitable T-splines
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REAL-VALUED PERIODIC WAVELETS: CONSTRUCTION ANDRELATION WITH FOURIER SERIES 被引量:3
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作者 Chen, HL Liang, XZ +1 位作者 Peng, SL Xiao, SL 《Journal of Computational Mathematics》 SCIE CSCD 1999年第5期509-522,共14页
In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the for... In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed. 展开更多
关键词 periodic wavelet MULTIRESOLUTION Fourier series linear independence
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Transcendence of Certain Trigonometric Series 被引量:2
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作者 Yao Chen ZHU Academy of Mathematics and System Sciences. The Chinese Academy of Sciences, Beijing 100080. P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2002年第3期481-488,共8页
In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The... In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The proof of the theorem is based on a criterion for linear independence over a number field. 展开更多
关键词 TRANSCENDENCE Trigonometric series linear independence Number field
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